The present invention relates generally to equalization techniques and equalizers for wireless communication systems, and more particularly, to Walsh Hadamard Transform domain equalization and equalizers.
Code Division Multiple Access (CDMA) systems, such as wireless communication networks, generate individual code channels using orthogonal code sets, such as Walsh codes. Multiple code channels generally are spread onto the same carrier frequency and transmitted as a combined signal. An individual receiver may recover selected ones of the individual code channels by correlating the combined received signal with the corresponding code(s).
Effective recovery of the individual code channels by the receivers depends on the orthogonality of the codes. Unfortunately, the typical transmission channel is time dispersive—i.e., multipath—and there is some loss of code orthogonality in the received signal, which represents a time-domain linear convolution of the transmitted signal and the transmission channel's impulse response. The impairment of code orthogonality, referred to as inter-path interference, compromises a receiver's ability to separate individual code channels from the combined signal.
The RAKE receiver is one type of communication receiver adapted for multipath reception, and it finds common use in CDMA systems. RAKE receivers offer the capability of resolving multipath components in a received signal. The typical RAKE receiver includes a plurality of RAKE fingers, and each RAKE finger detects a different multipath component using a correlation process that treats all other multipath components as interference. The RAKE receiver then computes a weighted sum of the individually detected multipath components according to maximal ratio combining principles to generate the RAKE output signal.
However, the ability of a RAKE receiver to resolve inter-path interference arising from multipath reception is limited. More particularly, RAKE receivers depend on bandwidth expansion (spread spectrum) to provide inter-path interference suppression. If the inter-path interference is not suppressed sufficiently, the RAKE receiver's diversity combining performance will be degraded. The residual, irreducible interference limits the achievable data rate for Walsh code multiplexed CDMA systems.
Other receiver types may offer performance advantages over RAKE receivers. For example, transmit/receive methods based on Orthogonal Frequency Division Multiplexing (OFDM) have been recognized for their capability of equalizing frequency-selective distortions using simple one-tap divisions in the frequency domain. Indeed, frequency domain equalization (FDE) is one feature that distinguishes OFDM receiver performance from that of a Walsh code multiplexed CDMA system that conventionally requires a RAKE receiver first to resolve the multiple signal components in a multipath signal and then combine them for diversity.
In contrast, an OFDM receiver does not need to resolve multipath components explicitly; rather it directly compensates the frequency-selective distortion of the multipath transmission channel in the Fourier transform domain (the frequency domain). Such operation exploits the duality existing between the linear time convolution of the transmitted signal and the transmission channel's impulse response and Fourier transform domain processing. Time-domain convolution equates to frequency domain multiplication, although an actual OFDM receiver may use one-tap division operations rather than de-convolution to perform frequency domain equalization of the received signal. Further, an OFDM receiver may use Discrete Fourier Transform (DFT) or Fast Fourier Transform (FFT) for received signal processing. The duality property of the DFT or the FFT has a slight difference, i.e., time-domain cyclic convolution corresponds to frequency domain point-wise multiplication.
Cyclic convolution does not naturally occur in signal transmission, which fundamentally is a linear convolution of the transmitted signal and the channel response, but it can be mimicked by manipulating the transmitted signal such that certain portions of it are repeated. These repeated portions of the transmitted signal sometimes are referred to as cyclic prefixes. When the cyclic prefixed transmit signal passes through the multipath channel, the linear convolution of channel impulse response will produce a received signal with a portion that is equivalent to cyclic convolution. Such operations are exploited in OFDM receiver processing based on the above-mentioned and well-known duality relationship between cyclic convolution in the time domain and point-wise multiplication in the discrete frequency domain.
However, while OFDM-based signal processing may offer certain performance advantages over RAKE-based processing in Walsh code multiplexed CDMA systems, it is not without its disadvantages. For example, OFDM signal transmission and reception requires fundamentally different transmitter and receiver structures to support OFDM's use of multiple carrier frequencies. Further, OFDM-based processing is not trivial. Other transmission and reception frameworks may offer the advantages of improved multipath equalization performance without requiring any fundamental departure from the basic transceiver architectures used in existing CDMA systems.
For example, transmitting signals based on Walsh code multiplexing can offer the equalization performance advantages of OFDM with the benefit of potentially simplified signal processing, while simultaneously complementing existing CDMA transmission methods. That is, with Walsh code multiplexed CDMA systems, the orthogonal basis functions are Walsh-Hadamard codes meaning that signal processing requires simple addition and subtraction operations, while in OFDM the basis functions are sinusoids meaning that signal processing requires more compute-intensive signal processing operations.
However, one problematic aspect of signal processing in the Walsh-Hadamard Transform (WHT) domain is the complicated and poorly understood relationship between the WHT domain processing corresponding to the time-domain convolution of the transmit signal and the channel impulse response and WHT domain. That is, conceptually, Walsh-Hadamard transforms and Fourier transforms both are based on orthogonal bases and have certain duality properties in the transform domain. For Fourier transform, the convolution theorem is well known, but such is not the case for the WHT domain. Therefore, the receiver operations needed for mitigating inter-path interference—i.e., cross correlations between the Walsh codes used to generate the transmitted data signal—can be difficult to discern or implement.